In a Young's double slit experiment, the intensities at two points, for the path differences (λ)/(4) and (λ)/(3) ( λ being the wavelength of light used) are I₁ and I₂ respectively. If I₀ denotes the intensity produced by each one of the individual slits, then (I₁+I₂)/(I₀) = __________. Numerical answer type. Work it out, then open the answer.

Answer: 3. For two equal slits, I = 4I₀cos ²φ/2 with φ = (2π)/(λ)Δ x. Δ x = (λ)/(4): φ = π/2, I₁ = 4I₀cos ² 45° = 2I₀ Δ x = (λ)/(3): φ = 2π/3, I₂ = 4I₀cos ² 60° = I₀ (I₁+I₂)/(I₀) = 3

In a Young's double slit experiment, the intensities at two points… | JEE Main 2023 (30 Jan, Shift 2)

Q65JEE Main 2023 · 30 JAN · SHIFT 2Medium

Superposition, Coherence & Intensity

In a Young's double slit experiment, the intensities at two points, for the path differences $\frac{\lambda}{4}$ and $\frac{\lambda}{3}$ ( $\lambda$ being the wavelength of light used) are $I_1$ and $I_2$ respectively. If $I_0$ denotes the intensity produced by each one of the individual slits, then $\frac{I_1+I_2}{I_0} =$ __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 3

For two equal slits, $I = 4I_0\cos^2\frac{\phi}{2}$ with $\phi = \frac{2\pi}{\lambda}\Delta x$ .
$\Delta x = \frac{\lambda}{4}$ : $\phi = \frac{\pi}{2}$ , $I_1 = 4I_0\cos^2 45^\circ = 2I_0$
$\Delta x = \frac{\lambda}{3}$ : $\phi = \frac{2\pi}{3}$ , $I_2 = 4I_0\cos^2 60^\circ = I_0$
$\frac{I_1+I_2}{I_0} = 3$

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